I’ve been thinking a lot lately about teaching a class, what would go into it, how I would grade it, and all that jazz. This, of course, leads me to think about how grades should be assigned, and what’s important. Obviously every aspect should have a purpose — handing out midterms without a unified idea behind what you want to do with the midterm is rather fruitless.

So I’m going to start by discussing my philosophy behind tests. I begin with a very important caveat: I have never taught a course as a lead instructor. This is based upon my own musings, and not on any actual experience. Anyone can feel free to share their personal experiences and wisdom with me; in fact, such shared information would be greatly appreciated.

Using the standard Socratic method I feel is so important in teaching, I will begin by posing a question: Why do we give midterm examinations?

Most students will give the argument that if there’s something out there that’s needed, it can be easily looked up in a book as needed. Prima facia, this looks like a legitimate argument. Of course, it has its merits. Memorizing the details of the solution for the magnetic field in a Helmholtz coil is rather fruitless, and it can be quickly looked up in any elementary physics textbook. But there are two fundamental flaws in this reasoning:

First of all, it assumes that the student has attained a sufficient mastery of the subject to be able to make use of the equation once it is located. This is not always the case, as is evident by the fact that, in my experience, open book tests usually shift the curve, it doesn’t skew it towards the higher end of the grading scale. Evidently, all the open book does for the majority of students is get them extra partial credit for writing down equations they hadn’t memorized, and it doesn’t cause everyone to suddenly do miraculously better.

Second, it assumes that the purpose of the test is to ‘pimp’ the student on information they should have memorized. Some tests may be used like this, but I tend to think that tests serve an entirely different purpose.

There is something to be said for quick recall of information, and being able to apply old information to a new problem on the fly. Certainly, if you are giving a presentation to your boss and he asks you something you didn’t anticipate, you will look like a fool if you “hummmm” and “haawwww” at the question for a few minutes, before giving an half-satisfactory answer. Tests give the instructor the ability to see how well the students grasp a fundamental concept, without allowing the student to consult with his/her peers, or searching through the book for the “right answer”. If properly written, the test also emphasizes that concepts are more important than facts, but at the same time concepts need facts to make sense.

The other thing tests give that homeworks don’t is pressure. In the real world, there are usually unreasonable deadlines that require quick thinking and recall under pressure. Homeworks are a difficult way to test this, and give the student experience doing this. The test, under time pressure, is the only way for the instructor to successfully pull this off.

Both of these are good reasons for why tests should be administered, but what kind of tests should be written? Obviously, from the above discussion, we can’t give out tests that require students to write down two line formulae and just compute the answer. Nor should it simply be a chain of trivial problems to test the students’ ability to churn out answers as quickly as possible.

In my view, for a one hour test, there should be three problems, one of them a trivial churn and compute problem (there’s something to be said for raw computation) and then two problems that are designed to make the students link together one concept and another. Frankly, making a test that can be finished off in the alotted time is silly. How can you differentiate the great students from the good ones? Ultimately, that’s what a grade is for, and it would be foolish to lose sight of this.

So here we are, a three problem test, focused primarily on filling in the details of some elaboration of the basic ideas. This does the trick, testing the student’s grasp of the material at a conceptual level, as well as the plug and chug skills required to actually solve the problems. I just hope that this philosophy works out at the end of the day, when it’s my turn to write the tests.